8x-3(2x-9)=7(2x-5)6x-1

Solution for 8x-3(2x-9)=7(2x-5)6x-1 equation:

8x-3(2x-9)=7(2x-5)6x-1

We move all terms to the left:

8x-3(2x-9)-(7(2x-5)6x-1)=0

We multiply parentheses

8x-6x-(7(2x-5)6x-1)+27=0


We calculate terms in parentheses: -(7(2x-5)6x-1), so:

7(2x-5)6x-1

We multiply parentheses

84x^2-210x-1

Back to the equation:

-(84x^2-210x-1)


We add all the numbers together, and all the variables

2x-(84x^2-210x-1)+27=0

We get rid of parentheses

-84x^2+2x+210x+1+27=0

We add all the numbers together, and all the variables

-84x^2+212x+28=0

a = -84; b = 212; c = +28;
Δ = b2-4ac
Δ = 2122-4·(-84)·28
Δ = 54352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{54352}=\sqrt{16*3397}=\sqrt{16}*\sqrt{3397}=4\sqrt{3397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(212)-4\sqrt{3397}}{2*-84}=\frac{-212-4\sqrt{3397}}{-168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(212)+4\sqrt{3397}}{2*-84}=\frac{-212+4\sqrt{3397}}{-168}
$